{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "vDJ4XzMqodTy"
      },
      "source": [
        "# Automatic Differentiation\n",
        "\n",
        "In the previous tutorial we introduced `Tensor`s and operations on them. In this tutorial we will cover [automatic differentiation](https://en.wikipedia.org/wiki/Automatic_differentiation), a key technique for optimizing machine learning models."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "GQJysDM__Qb0"
      },
      "source": [
        "## Setup\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        },
        "colab_type": "code",
        "id": "OiMPZStlibBv"
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "tf.enable_eager_execution()\n",
        "\n",
        "tfe = tf.contrib.eager # Shorthand for some symbols"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "1CLWJl0QliB0"
      },
      "source": [
        "## Derivatives of a function\n",
        "\n",
        "TensorFlow provides APIs for automatic differentiation - computing the derivative of a function. The way that more closely mimics the math is to encapsulate the computation in a Python function, say `f`, and use `tfe.gradients_function` to create a function that computes the derivatives of `f` with respect to its arguments. If you're familiar with [autograd](https://github.com/HIPS/autograd) for differentiating numpy functions, this will be familiar. For example: "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        },
        "colab_type": "code",
        "id": "9FViq92UX7P8"
      },
      "outputs": [],
      "source": [
        "from math import pi\n",
        "\n",
        "def f(x):\n",
        "  return tf.square(tf.sin(x))\n",
        "\n",
        "assert f(pi/2).numpy() == 1.0\n",
        "\n",
        "\n",
        "# grad_f will return a list of derivatives of f\n",
        "# with respect to its arguments. Since f() has a single argument,\n",
        "# grad_f will return a list with a single element.\n",
        "grad_f = tfe.gradients_function(f)\n",
        "assert tf.abs(grad_f(pi/2)[0]).numpy() \u003c 1e-7"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "v9fPs8RyopCf"
      },
      "source": [
        "### Higher-order gradients\n",
        "\n",
        "The same API can be used to differentiate as many times as you like:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "height": 276
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 730,
          "status": "ok",
          "timestamp": 1527005655565,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 420
        },
        "id": "3D0ZvnGYo0rW",
        "outputId": "e23f8cc6-6813-4944-f20f-825b8a03c2ff"
      },
      "outputs": [
        {
          "data": {
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5nzUnrbzzj51MmZnKmUvGhbCnbQn1eH79RR77d5Zx+Q2zSEju+1F0u7YUsXVj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\nF3bGGIswXNgZYyzC/Be68EGj7hfMcwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f385e198650\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def f(x):\n",
        "  return tf.square(tf.sin(x))\n",
        "\n",
        "def grad(f):\n",
        "  return lambda x: tfe.gradients_function(f)(x)[0]\n",
        "\n",
        "x = tf.lin_space(-2*pi, 2*pi, 100)  # 100 points between -2π and +2π\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.plot(x, f(x), label=\"f\")\n",
        "plt.plot(x, grad(f)(x), label=\"first derivative\")\n",
        "plt.plot(x, grad(grad(f))(x), label=\"second derivative\")\n",
        "plt.plot(x, grad(grad(grad(f)))(x), label=\"third derivative\")\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "-39gouo7mtgu"
      },
      "source": [
        "## Gradient tapes\n",
        "\n",
        "Every differentiable TensorFlow operation has an associated gradient function. For example, the gradient function of `tf.square(x)` would be a function that returns `2.0 * x`.  To compute the gradient of a user-defined function (like `f(x)` in the example above), TensorFlow first \"records\" all the operations applied to compute the output of the function. We call this record a \"tape\". It then uses that tape and the gradients functions associated with each primitive operation to compute the gradients of the user-defined function using [reverse mode differentiation](https://en.wikipedia.org/wiki/Automatic_differentiation).\n",
        "\n",
        "Since operations are recorded as they are executed, Python control flow (using `if`s and `while`s for example) is naturally handled:\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        },
        "colab_type": "code",
        "id": "MH0UfjympWf7"
      },
      "outputs": [],
      "source": [
        "def f(x, y):\n",
        "  output = 1\n",
        "  for i in range(y):\n",
        "    output = tf.multiply(output, x)\n",
        "  return output\n",
        "\n",
        "def g(x, y):\n",
        "  # Return the gradient of `f` with respect to it's first parameter\n",
        "  return tfe.gradients_function(f)(x, y)[0]\n",
        "\n",
        "assert f(3.0, 2).numpy() == 9.0   # f(x, 2) is essentially x * x\n",
        "assert g(3.0, 2).numpy() == 6.0   # And its gradient will be 2 * x\n",
        "assert f(4.0, 3).numpy() == 64.0  # f(x, 3) is essentially x * x * x\n",
        "assert g(4.0, 3).numpy() == 48.0  # And its gradient will be 3 * x * x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "aNmR5-jhpX2t"
      },
      "source": [
        "At times it may be inconvenient to encapsulate computation of interest into a function. For example, if you want the gradient of the output with respect to intermediate values computed in the function. In such cases, the slightly more verbose but explicit [tf.GradientTape](https://www.tensorflow.org/api_docs/python/tf/GradientTape) context is useful. All computation inside the context of a `tf.GradientTape` is \"recorded\".\n",
        "\n",
        "For example:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        },
        "colab_type": "code",
        "id": "bAFeIE8EuVIq"
      },
      "outputs": [],
      "source": [
        "x = tf.ones((2, 2))\n",
        "  \n",
        "# TODO(b/78880779): Remove the 'persistent=True' argument and use\n",
        "# a single t.gradient() call when the bug is resolved.\n",
        "with tf.GradientTape(persistent=True) as t:\n",
        "  # TODO(ashankar): Explain with \"watch\" argument better?\n",
        "  t.watch(x)\n",
        "  y = tf.reduce_sum(x)\n",
        "  z = tf.multiply(y, y)\n",
        "\n",
        "# Use the same tape to compute the derivative of z with respect to the\n",
        "# intermediate value y.\n",
        "dz_dy = t.gradient(z, y)\n",
        "assert dz_dy.numpy() == 8.0\n",
        "\n",
        "# Derivative of z with respect to the original input tensor x\n",
        "dz_dx = t.gradient(z, x)\n",
        "for i in [0, 1]:\n",
        "  for j in [0, 1]:\n",
        "    assert dz_dx[i][j].numpy() == 8.0"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "DK05KXrAAld3"
      },
      "source": [
        "### Higher-order gradients\n",
        "\n",
        "Operations inside of the `GradientTape` context manager are recorded for automatic differentiation. If gradients are computed in that context, then the gradient computation is recorded as well. As a result, the exact same API works for higher-order gradients as well. For example:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        },
        "colab_type": "code",
        "id": "cPQgthZ7ugRJ"
      },
      "outputs": [],
      "source": [
        "# TODO(ashankar): Should we use the persistent tape here instead? Follow up on Tom and Alex's discussion\n",
        "\n",
        "x = tf.constant(1.0)  # Convert the Python 1.0 to a Tensor object\n",
        "\n",
        "with tf.GradientTape() as t:\n",
        "  with tf.GradientTape() as t2:\n",
        "    t2.watch(x)\n",
        "    y = x * x * x\n",
        "  # Compute the gradient inside the 't' context manager\n",
        "  # which means the gradient computation is differentiable as well.\n",
        "  dy_dx = t2.gradient(y, x)\n",
        "d2y_dx2 = t.gradient(dy_dx, x)\n",
        "\n",
        "assert dy_dx.numpy() == 3.0\n",
        "assert d2y_dx2.numpy() == 6.0"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "4U1KKzUpNl58"
      },
      "source": [
        "## Next Steps\n",
        "\n",
        "In this tutorial we covered gradient computation in TensorFlow. With that we have enough of the primitives required to build an train neural networks, which we will cover in the [next tutorial](https://github.com/tensorflow/models/tree/master/official/contrib/eager/python/examples/notebooks/3_neural_networks.ipynb)."
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "default_view": {},
      "name": "Automatic Differentiation",
      "provenance": [],
      "version": "0.3.2",
      "views": {}
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
